The time-dependent characteristic function for the vibratlonal quanta of two ions separately trapped in two caacaded optical eavities is obtained analytieally beyond the bad cavity linit, in which tfie motional mode of the ion in the first cavfiy is coupled to lhe cavity, field via an effective parametrc interacion and that of the ion in the second cavity" via a liaear-mixing interaction as proposed by Peng and Parkias Pfiys. Rev. A 65, 062323 (2002l]. It is fond, that the two ions develop in a two-mode mixed Gaussian entangle state if there exists a unidirecfional coupling from the first cavitv to the seecond one.

Spontaneous emission of an atom with two close upper levels arid one lower level in a multilayer dielectric medium, and quantum interference between transitions form the upper leves to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to tbe interfaces of the dielectric layers, the vancuum had an anisotropic spatial structure, and quantum interference between the two decay channels can appear even if the two dipole matrix elemeats are ortbogonal to each other. If the atom is pLaced in a three-layer dielectric plate cavity, a strong quantum interference interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.

We investigate the effect of the dipole-dipole interaction on the dynamic properties and the atomic coherent trapping of a two-identical atom system in the presence of a laser field by means of quantum electrodynamics theory, The influence of the dipole-dipole interaction on the collapses and revivats of the atomic population is revealed. The conditions of the atomic eoherent trapping are given. A way to measure optically the coupling strength between the atoms is pointed out. Wc also show that the cffect of the dipole-dipole interaction may be screened duc to the coherent field in certain atomic superposition states.

In this paper, we have investigated the time evolution of |he phase operator of the radiation field in the Jaynes-Cummings model with and without tfie rotating-wave approximation, making use of the phase formalism of Barnett and Pegg [J. Mod. Opt. 56, 7 (1989); Phys. Rev. A 39, 1665 (1989)]. We verify by an analytical method that the atomic Rabi oscillation leads to phase dissipation of the radiation field, and also that the effect of the virtual-photon field can exhibit quantum fluctuations in the atomfield-coupling system and lead to a Frequency shift of the radiation field.

In this paper, we have investigated the influence of the cvunler-rotating terms on the squeezing of light in the two photon layaes-Cummings mcodel by means of the nonrelativistic QED. We verified that the effect af the virtual-photon field increases the squeezing. The relations between the degree of squeezing and the frequency of field, the mean photon number, and the atom-field coupling constant have alsp been analyzed.